What is the largest 25-digit number that can be divided by 2 and 5 without any remainder?

14. Number of Zeros in 1 × 2 × 3 ×⋯× 24 × 25

How many zeros are there at the end of the product 1 × 2 × 3 ×⋯× 24 × 25?

15. The Chocolate Bar

Given a 25-piece square chocolate bar, how many snaps are required to break the bar into its individual pieces?

16. A Creative Thinking Question

It is late on Christmas Eve and little Noel is waiting the Christmas tree to be finished. At exactly what time will this happen?

17. Christmas and Halloween

Prove that Oct. 31 = Dec. 25.

18. Divisibility by 25

Show that, if n is a positive integer, 16n + 10n – 1 is divisible by 25.

19. A Pair of Christmas AlphameticsIn each case, replace each letter with a digit, different letters being different digits.(a) SANTA - CLAUS = XMAS

(b) A + MERRY + XMAS = TURKEY

20. A Sum of Squares

Find the value of 1² – 2² + 3² – 4² +⋯+ 25².

21. Number of Rectangles

A board has 25 squares. How many individual rectangles are there in all?

22. A Christmas Party

At a Christmas party, each child brought a present. Presents were put in a large basket. All presents were different but identically wrapped. Going home, each child randomly selected a present from the basket. What is the expected number of children who carry home their own presents?

23. How Many Lines?

Using only horizontal and vertical lines, what is the most number of straight lines you can draw between the dots in a 5 × 5 grid without lifting your pencil?

24. A Table of 25 Boys and 25 Girls

A total of 25 boys and 25 girls sit around a table. Show that it is always possible to find a person both of whose neighbors are girls.

About Me

Yan Kow Cheong (kcyan.mathplus@gmail.com and @MathPlus & @Zero_Math) is a math coach, writer, and editor. A math consultant for MathPlus Consultancy, he specializes in both adult and recreational math education. He conducts recreational and competition math courses and workshops for schools and enrichment centers, and educates the public against innumeracy and pseudoscience.

He has ghostwritten and edited both local and foreign textbooks and assessment titles for students, teachers, and parents. Some of his publications are Additional Maths 360, Mathematical Quickies & Trickies, Aha! Math, and CHRISTmaths: A Creative Problem Solving Math Book. http://tinyurl.com/3lfuzsf

His forthcoming titles are: What's Wrong? A Comedy of Mathematical Errors and Who Took My Calculator?. His academic interests involve research in math education, in particular, the psychology of learning and teaching mathematics, and creative problem solving. He is a life member of both the Singapore Mathematical Society (SMS) and the Association of Mathematics Educators (AME). He is also a member of The Association of Christians in the Mathematical Sciences (ACMS).